Number Theory & Computation
(MCQ):
What is the value of (16) 1/2?
A) 4
B) 8
C) 2
D) 1
A) 4
The power of 1/2 is the same as the square root. The square root of 16 is 4.
(MCQ):
What is the simplified form of x³×x⁵?
A) x8
B) x15
C) x²
D) x1.5
A) x8
When multiplying powers with the same base, you add the exponents: 3+5=8.
(True or False):
If the exchange rate is $1.00 USD = 6.75 TTD, then $200.00 USD is worth $1350.00 TTD.
True
To convert from USD to TTD, you multiply by the exchange rate: 200×6.75=1350.
(True or False):
A right-angled triangle can have two right angles.
False
The sum of angles in any triangle is 180 degrees. If a triangle had two right angles (90 degrees each), their sum would already be 180 degrees, leaving no space for the third angle.
MCQ):
If a linear graph passes through the points (0,2) and (2,6), what is its y-intercept?
A) 0
B) 2
C) 6
D) 4
B) 2
The y-intercept is the point where the graph crosses the y-axis. This always happens when the x-coordinate is 0. The point is given as (0,2).
True or False:
The Highest Common Factor (H.C.F.) of 12 and 18 is 6.
True
The factors of 12 are 1, 2, 3, 4, 6, 12. The factors of 18 are 1, 2, 3, 6, 9, 18. The common factors are 1, 2, 3, and 6. The highest of these is 6.
(True or False):
If 2x−5=7, then x=6.
True
To solve for x, you first add 5 to both sides: 2x=12. Then you divide by 2: x=6.
(MCQ):
An item costs $100. If you get a 15% discount, what is the new price?
A) $85
B) $90
C) $115
D) $15
A. $85
First, calculate the discount amount: 15% of 100=0.15×100=15. Then, subtract the discount from the original price: 100−15=85.
(Fill in the Blanks):
The volume of a rectangular prism with a length of 5 cm, a width of 4 cm, and a height of 3 cm is _______ cm3.
60
The formula for the volume of a rectangular prism is V=L×W×H. V=5×4×3=60 cm³..
True or False:
The gradient of the line y=3x−5 is 5.
False
In the equation of a straight line, y=mx+c, the gradient is represented by 'm'. In this equation, m is 3, not 5.
(True or False):
The number 1.25×10⁻³ is equivalent to 0.00125.
True
A negative power of 10 means you move the decimal point to the left. The power of −3 means you move the decimal point three places to the left.
MCQ
The solution to the inequality 3x−2>10 is x>_______.
A. 60
B. 8
C. 16
D. 4
D. 4
To solve the inequality, you first add 2 to both sides: 3x>12. Then you divide by 3: x>4.
MCQ
A loan of $5,000 is taken at a simple interest rate of 10% per annum for 2 years. The total simple interest is _________ dollars.
A. 100
B. 1000
C. 500
D. 5000
B. 1000
The formula for simple interest is I=P×R×T.
P (Principal) = 5,000
R (Rate) = 10%=0.10
T (Time) = 2 years
I=5000×0.10×2=1,000.
(MCQ):
What is the perimeter of a rectangle with a length of 10 m and a width of 5 m?
A) 15 m
B) 30 m
C) 45 m
D) 50 m
B) 30 m
The perimeter of a rectangle is P=2(L+W). P=2(10+5)=2(15)=30 m.
(MCQ):
A graph showing the relationship between two variables that are not directly proportional would not pass through the origin.
A) y=2x
B) y=x2
C) y=−x
D) y=2x+1
D) y=2x+1
In a proportional relationship, when one variable is zero, the other must also be zero, meaning the graph passes through the origin (0,0). The equation y=2x+1 has a y-intercept of 1, so it does not pass through the origin.
(Fill in the Blanks):
If A={1,2,3,4} and B={3,4,5}, then A∪B={1,2,_____________}.
3, 4, 5
The symbol ∪ represents the union of two sets, which includes all the elements from both sets without repeating any elements.
(MCQ):
Expand the expression (x+2)(x−3).
A) x² +5x−6
B) x² − x − 6
C) x² + x − 6
D) x² − x + 6
B) x² − x − 6
Use the FOIL method (First, Outer, Inner, Last):
First: x × x = x²
Outer: x −3=−3x
Inner: 2 × x=2x
Last: 2 ×−3=−6
Combine the terms: x²−3x+2x−6=x²−x−6.
MCQ
A television costs $2,500 cash or can be bought on hire purchase with a deposit of $500 and 12 monthly payments of $200. What is the total cost of the television on hire purchase?
A) $2,400
B) $2,900
C) $3,000
D) $2,500
B) $2,900
The total hire purchase cost is the deposit plus the total of the monthly payments. Total payments = 12×200=2,400. Total cost = 500+2,400=2,900.
True or False:
The circumference of a circle is the same as its perimeter.
True
Circumference is the specific term for the perimeter of a circle. They both refer to the distance around the outside of a shape.
True or False:
The graph of a quadratic function is a straight line.
False
A quadratic function, such as y=x²+2x+1, forms a parabola, which is a U-shaped curve, not a straight line.
What is the value of 1/2 + 1/3?
A) 1/5
B) 2/5
C) 5/6
D) 2/3
5/6
To add fractions, you must find a common denominator, which is 6. 1/2=3/6 and 1/3=2/6. Adding them gives you 3/6 + 2/6 = 5/6.
MCQ
Which of the following is a quadratic equation?
A) 2x−5=0
B) x³−4x²+2=0
C) x²+5x=10
D) x=5y+2
C) x²+5x=10
A quadratic equation is a polynomial equation of the second degree, meaning the highest power of the variable is 2. Option C is the only one that fits this description.
(Fill in the Blanks):
An employee earns an hourly rate of $20 and works 40 hours a week. Their gross weekly wage is _______ dollars.
800
Gross weekly wage is calculated by multiplying the hourly rate by the number of hours worked: 20×40=800.
(Fill in the Blanks):
In a right-angled triangle, the side opposite the right angle is called the _____________.
hypotenuse
The hypotenuse is the longest side of a right-angled triangle and is always opposite the 90-degree angle.
The graph of the function f(x)=x²−4x+3 intersects the y-axis at which point?
(0, 3)
The graph of a function intersects the y-axis when the x-coordinate is 0. To find the y-intercept, substitute x=0 into the function:f(0)=(0)²−4(0)+3=3. The point is (0, 3).